Plasma electron temperature measuring method and device

ABSTRACT

A laser beam with a wavelength capable of exciting atoms of helium in the metastable state is directed to a generated plasma, and atoms in the metastable state are excited. Absorption amount information representing the amount of laser beam absorbed is acquired, and the density of atoms of helium in the metastable state in the plasma is computed from the absorption amount. The emissions of light from helium gas in the plasma caused by transition from two different excited states to the lower level are measured, and the ratio between the intensities of the emissions is determined. The electron temperature of the produced plasma is computed from the computed density of the atoms of helium gas in the metastable state and the computed emission intensity ratio. With this, the plasma electron temperature can be computed with a relatively high accuracy irrespective of the condition of the plasma atmosphere.

CROSS-REFERENCE TO RELATED APPLICATIONS

This U.S. National stage application claims priority under 35 U.S.C. §119(a) to Japanese Patent Application No. 2007-091308, filed in Japan on Mar. 30, 2007, the entire contents of which are hereby incorporated herein by reference.

TECHNICAL FIELD

The present invention relates to plasma measurement technology, specifically to a method and a device which measures plasma electron temperature.

BACKGROUND ART

Recently, the so-called plasma processing has been actively employed for, e.g., etching and film formation on a semiconductor and a glass substrate. To achieve a desired condition in the plasma processing, it is important to control fundamental quantity (i.e., physical quantity) of plasma itself. For example, efficient plasma processing for purposes such as etching and film formation, will be achieved if a spatial distribution and a time-dependent shift of plasma electron temperature can be measured for plasma, which is generated for executing the plasma processing such as etching and film formation, and plasma electron temperature can be controlled based on the measurement result. In executing the plasma processing, plasma measurement (plasma assessment), i.e., obtainment of the fundamental quantity (i.e., physical quantity) of plasma itself (e.g., plasma electron temperature), is important.

Therefore, a variety of methods of measuring plasma electron temperature, including e.g., the Langmuir probe method and the Thomson scattering method, have been conventionally used. In the Langmuir probe method, however, a metal probe is required to be inserted into plasma. A drawback accordingly is occurred in that metal is polluted by the plasma. Therefore, the Langmuir probe method has not been suitable for plasma measurement in the actual plasma processing (e.g., etching and film formation). On the other hand, a measurement device, having complex structure, is required for the Thomson scattering method. Additionally, the Thomson scattering method is a technically difficult method. Therefore, it has been impossible to make a measurement of the plasma with a simple device configuration at relatively low cost in the plasma processing.

Japan Laid-open Patent Publication No. H10-83893 and Japan Laid-open Patent Publication No. 2006-318800 describe other methods of measuring plasma electron temperature. Japan Laid-open Patent Publication No. H10-83893 describes an example of a method of measuring plasma electron temperature using so-called emission spectroscopy. According to the method of measuring plasma electron temperature described in Japan Laid-open Patent Publication No. H10-83893, measurements are made of light emission of atoms in plasma due to a lower level transition process of the atoms from the first excited state and light emission of atoms in plasma due to other lower level transition process of the atoms from the second excited state. Plasma electron temperature is subsequently computed based on emission intensity ratio between the above the two light emissions. In the method described in Japan Laid-open Patent Publication No. H10-83893, plasma electron temperature is computed based on an assumption that the number of atoms excited at a predetermined energy level in plasma is based on rules of statistical mechanics including the Boltzmann distribution when the plasma is in thermal equilibrium. In the method described in Japan Laid-open Patent Publication No. 2006-318800, on the other hand, laser light, having suitable wavelength enabling to excite atoms of argon gas in a metastable state, is irradiated to plasma of the argon gas which is generated in a chamber for measuring transmittance of the laser light. Density of the atoms in the metastable state is computed based on information of the measured transmittance of the laser light. Moreover, plasma electron temperature is computed in a limited condition, using the computed density of the atoms in the metastable state and the rate equation for determining the metastable state.

SUMMARY OF THE INVENTION

<Technical Problem to be Solved by the Invention>

However, there is large error between actual plasma electron temperature and electron temperature computed with the assumption that the number of atoms excited at a predetermined energy level in plasma is based on the Boltzmann distribution as seen in the method described in Japan Laid-open Patent Publication No. H10-83893. In a method based on emission spectroscopy, it is known that computed plasma electron temperature generally lacks of reliability, and accurate electron temperature can be rarely obtained.

On the other hand, in the method using the rate equation for determining the metastable state, which is described in Japan Laid-open Patent Publication No. 2006-318800, computation of plasma electron temperature is only available under the following assumptions: electron density in a chamber (i.e., plasma generation space) is equal to or greater than 10¹⁰/cm³; gas pressure in the plasma generation space within the chamber is equal to or greater than 10 Pa (e.g., equal to or greater than 100 mTorr (approximately 13 Pa)); diffusion distance (i.e., mean free path of atoms of argon of a metastable state in plasma) is equal to or greater than 1cm; or plasma atmosphere satisfies all the above conditions or two or more of the above conditions. Moreover, in the method described in Japan Laid-open Patent Publication No. 2006-318800, it is necessary to preliminarily obtain highly accurate collision quenching coefficient between Ar (argon) atoms in the metastable state and the ambient gas. In the method described in Japan Laid-open Patent Publication No. 2006-318800, error of the computed plasma electron temperature has been relatively large in some conditions of the plasma atmosphere or when reliable information is not obtained for the quenching coefficient.

In response to this, it is an object of the present invention to provide a method of measuring plasma electron temperature, which is capable of computing plasma electron temperature with relatively high accuracy, regardless of a condition of plasma atmosphere. Additionally, it is another object of the present invention to provide a relatively cheap plasma electron temperature measuring device having relatively simple structure, which is capable of computing plasma electron temperature with relatively high accuracy, regardless of a condition of plasma atmosphere and without obtaining reliable information of a quenching coefficient.

<Solution to Problem>

To achieve the aforementioned objects, the present invention provides a method of measuring electron temperature of plasma to be generated. The method includes the steps of: providing at least helium gas to a predetermined container to generate plasma in the predetermined container; irradiating laser light to the generated plasma, the laser light having wavelength which is capable of exciting atoms of the helium gas in a metastable state, to excite the atoms in the metastable state; obtaining absorption amount information representing an amount of the laser light absorbed by the atoms in the metastable state; computing density of the atoms of the helium gas in the metastable state in an irradiation area of the laser light in the plasma based on the absorption amount information; measuring each of light emissions due to lower level transition processes from two different excited states of the helium gas in the plasma and computing an emission intensity ratio between the light emissions; and computing electron temperature of the generated plasma based on the emission intensity ratio and the computed density of the atoms of the helium gas in the metastable state.

Moreover, the method preferably includes the steps of: irradiating laser light to the generated plasma, the laser light having wavelength which enables to excite the atoms of the helium gas in the metastable state, to excite the atoms in the metastable state; and obtaining information of a distribution of induced fluorescence intensity in the irradiation area of the laser light, the induced fluorescence intensity representing intensity of induced fluorescence from the atoms in the metastable state which is caused by irradiation of the laser light. Simultaneously, in the step of computing density of the atoms in the metastable state, a distribution of density of the atoms in the metastable state in the irradiation area of the laser light is at least computed based on the absorption amount information and the information of the distribution of the induced fluorescence intensity.

Furthermore, in the step of computing density of the atoms of the helium gas in the metastable state, density of the atoms in each of states 2¹S₀ and 2³S₁ is preferably computed as the density of the atoms in the metastable states. Simultaneously, in the step of computing the emission intensity ratio, the emission intensity ratio is preferably computed by measuring a light emission due to lower level transition processes from a state 4³D, which is a first excited state, to a state 2³P⁰ and a light emission due to a lower level transition process from a state 3³D, which is a second excited state, to the state 2³P⁰.

Alternatively, in the step of the computing density of the atoms in the metastable state, density of the atoms in each of states 2¹S₀ and 2³S₁ is preferably computed as the density of the atoms in the metastable state. Simultaneously, in the step of computing the emission intensity ratio, the emission intensity ratio is preferably computed by measuring a light emission due to a lower level transition process from a state 4³S, which is a first excited state, to a state 2³P⁰ and a light emission due to a lower level transition process from a state 3³S, which is a second excited state, to the state 2³P⁰.

In the step of computing the electron temperature, the plasma electron temperature is preferably computed using the following formula (1).

$\begin{matrix} \left\lbrack {{Formula}\mspace{14mu} 1} \right\rbrack & \; \\ \left. \begin{matrix} {\frac{{k_{{ex}\; 0}^{A}n_{0}} + {\sum\limits_{m = 1}{k_{exm}^{A}n_{m}}}}{{k_{{ex}\; 0}^{B}n_{0}} + {\sum\limits_{m = 1}{k_{exm}^{B}n_{m}}}} = {\frac{A^{A}}{A^{B}} \cdot \frac{n_{A}^{*}}{n_{B}^{*}}}} \\ {\frac{I_{A}}{I_{B}} = {\frac{g^{A}}{g^{B}} \cdot \frac{\lambda^{B}}{\lambda^{A}} \cdot \frac{A_{i}^{A} \cdot n_{A}^{*}}{A_{i}^{B} \cdot n_{B}^{*}}}} \end{matrix} \right\} & (1) \end{matrix}$ In the formula (1),

each of numerals relates to the atoms of the helium gas in the plasma;

“I_(A)” represents a measured value of intensity of the light emission due to a lower level transition process from a first excited state A, whereas “I_(B)” represents a measured value of intensity of the light emission due to a lower level transition process from a second excited state B;

“A_(i) ^(A)” represents an Einstein A-coefficient of the light emission due to the lower level transition process from the first excited state A, whereas “A_(i) ^(B)” represents an Einstein A-coefficient of the light emission due to the lower level transition process from the second excited state B;

“A^(A)” represents an inverse of a radiative lifetime of the atoms in the first excited state A, which is represented by the sum of Einstein A-coefficients in a plurality of natural transition processes from the first excited state A, whereas “A^(B)” represents an inverse of a radiative lifetime of the atoms in the second excited state B, which is represented by the sum of Einstein A-coefficients in a plurality of natural transition processes from the second excited state B;

“n_(m)” represent the computed density of the atoms in the m-th metastable state; “n₀” represents density of the atoms in a ground state;

“n_(A) ^(*)” represents density of the atoms in the first excited state A; and “n_(B) ^(*)” represents density of the atoms in the second excited state B;

“k^(A) _(ex0)” represents an electron impact excitation rate constant from the ground state to the first excited state A, whereas “k^(A) _(exm)” represents an electron impact excitation rate constant from the m-th metastable state to the first excited state A;

“k^(B) _(ex0)” represents an electron impact excitation rate constant from the ground state to the second excited state B, whereas “k^(B) _(exm)” represents an electron impact excitation rate constant from the m-th metastable state to the second excited state B, and “k^(A) _(ex0),” “k^(A) _(exm),” “k^(B) _(ex0),” and “k^(B) _(exm)” are functions of the plasma electron temperature;

“g^(A), g^(B)” are functions of wavelengths λ^(A) and λ^(B), each representing solid angle and quantum efficiency of an observation system in each of the excited states A and B, and “λ^(A), λ^(B)” are wavelengths of light to be measured in the excited states A and B.

Furthermore, the rate constant k^(a) _(exb) to be used in the step of computing the electron temperature is preferably represented by the following formula (2) and the plasma electron temperature is computed using the formula (1). [Formula 2] k _(exb) ^(a) =∫vσ _(exb)(v)f(v)dv  (2) In the formula (2),

“a” represents “A” or “B”, whereas “b” represents “0” or “m”; and

“σ^(a) _(exb)” represents cross section in each of the excitation processes; “v” represents electron velocity; and “f(v)” represents an electron energy distribution function.

Furthermore, in the step of obtaining the absorption amount information, transmittance of the laser light irradiated to the plasma is preferably obtained as the absorption amount information representing the amount of absorption of the laser light.

Furthermore, in the step of obtaining the absorption amount information, transmittance I_(t)/I_(0(m)) of the laser light is preferably computed by obtaining intensity I₀ of laser light to be irradiated to the plasma for exciting the atoms in the m-th metastable state and intensity I₁ of the laser light which has transmitted through the plasma. Simultaneously, in the step of computing the density of the atoms of the helium gas in the metastable state, density n_(m) of the atoms of the helium gas in the metastable state in the plasma is preferably computed based on the transmittance I_(t)/I_(0(m)) of the laser light and the following formula (3).

$\begin{matrix} \left\lbrack {{Formula}\mspace{14mu} 3} \right\rbrack & \; \\ {\frac{I_{t}}{I_{0{(m)}}} = {\exp\left\{ {{- {\sigma_{exm}(v)}}n_{m}1} \right\}}} & (3) \end{matrix}$ In the formula (3), “σ_(exm)” represents absorption cross section of the atoms in the m-th metastable state;

“l” represents length of a transmitting path of the laser light through the plasma; and

“n_(m)” represents density of the atoms in the m-th metastable state.

The present invention also provides a device for measuring plasma electron temperature. The device measures electron temperature of plasma generated in a predetermined container. The device includes: means for providing at least helium gas to the predetermined container for generating plasma while the helium gas is kept in the predetermined container; laser light irradiation means for irradiating laser light to plasma generated in the predetermined container, the laser light having wavelength which is capable of exciting atoms of the helium gas in a metastable state, to excite the atoms of the helium gas in the metastable state; means for obtaining absorption amount information representing an amount of the laser light absorbed by the atoms of the helium gas in the metastable state; means for computing density of the atoms of the helium gas in the metastable state in an irradiation area of the laser light in the plasma based on the absorption amount information; means for measuring each of light emissions due to lower level transition processes from two different excited states of the helium gas in the plasma and computing an emission intensity ratio between the light emissions; and means for computing electron temperature of the generated plasma based on the ratio between intensity of the light emissions and the density of the atoms of the helium gas in the metastable state computed by the means for computing the density.

EFFECTS OF INVENTION

According to the present invention, plasma electron temperature can be computed based on both of density of atoms in a metastable state in the plasma and density of the atoms in an excited state in the plasma using a relatively cheap measurement device which has a relatively simple structure. According to the present invention, plasma electron temperature can be computed with relatively high accuracy, compared to both of a conventional method of computing electron temperature only based on density of the atoms in a metastable state in the plasma and a conventional method of computing electron temperature only based on density of the atoms in an excited state in the plasma. Moreover, a spatial distribution of the electron temperature of the generated plasma can be obtained with relatively high accuracy.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 includes schematic diagrams for explaining structure of an example plasma processing apparatus provided with a device for measuring plasma electron temperature according to the present invention. FIG. 1A is a schematic perspective view whereas FIG. 1B is a schematic cross-sectional top view.

FIG. 2 is an example diagram for illustrating a variety of states of atoms of Helium gas in plasma.

FIG. 3 is a schematic block diagram of a measurement and control unit in the plasma processing apparatus illustrated in FIG. 1.

FIG. 4 is a flowchart for illustrating an example of plasma processing to be executed by the plasma processing apparatus illustrated in FIG. 1 together with an example of measurement of plasma electron temperature according to the present invention.

FIG. 5 is an example of light intensity distribution data of induced fluorescence generated by excitation using laser light L_(m) in a laser light irradiation area, which is obtained by the measurement control unit in the plasma processing apparatus illustrated in FIG. 1.

DETAILED DESCRIPTION OF THE INVENTION

A method and a device for measuring plasma electron temperature according to the present invention will be hereinafter explained in detail. FIG. 1 is a schematic diagram for illustrating structure of an example of plasma processing apparatus according to the present invention, provided with a device for measuring plasma electron temperature. Specifically, FIG. 1 A is a schematic perspective view of a plasma processing apparatus 10 whereas FIG. 1B is a schematic cross-sectional top view of the plasma processing apparatus 10.

The plasma processing apparatus 10, illustrated in FIG. 1, has a plasma generation section 14 generating plasma P in the interior of a reaction container 12 and executes a plasma processing on a processing target substrate (e.g., a semiconductor substrate and a glass substrate) disposed in the interior of the reaction container 12. Additionally, the plasma processing apparatus 10 is provided with a measurement unit 30, a measurement control unit 20 and a gas providing section 11. The measurement unit 30 measures a variety of information of the plasma P generated in the interior of the reaction container 12. The measurement control unit 20 obtains the measured information and controls the plasma P to be generated by the plasma generation section 14. The gas providing section 11 is provided with a gas canister and gas flow rate regulation means (not illustrated in the figure).

The reaction container 12 is a high vacuum chamber. For example, discharge means (not illustrated in the figure), composed of a rotary pump, a turbo-molecular pump and the like, discharges gas in the reaction container 12. The interior of the reaction container 12 is thereby allowed to be in a high vacuum state. The reaction container 12 is not herein limited to a vacuum chamber. For example, the plasma generation section 14 may be capable of generating plasma under the atmospheric pressure. Gas is provided into the interior of the reaction container 12 from the gas providing section 11 through a pipe. The present invention has one of the features that gas to be provided in the interior of the reaction container 12 include at least helium (He) gas in addition to processing gas required for film formation and etching (i.e., TEOS gas, oxygen gas or silane gas). The helium gas serves as an object to be measured (measurement target) to obtain information required to measure plasma electron temperature. A wall of the reaction container 12 is provided with a transparent laser incident window 16 a for a variety of laser light L_(m), a transparent laser exit window 16 b and a transparent emission observation window 18. Silicon, glass and the like are disposed in the windows 16 a, 16 b and 18. Additionally, the reaction container 12 is provided with a pressure sensor (not illustrated in the figure) for measuring pressure in the interior of the reaction container 12.

The plasma generation section 14 is composed of two flat-plate electrodes disposed in parallel to each other, for instance. When a plasma control section 26, which will be described later, in the measurement control unit 20 applies high-frequency voltage to the two parallel flat-plate electrodes, plasma P is generated in a gap between the parallel flat-plate electrodes. In the plasma processing device 10, a plasma film formation processing or a plasma etching processing will be executed on a semiconductor substrate or a glass substrate disposed in the clearance between the two parallel flat-plate electrodes, for instance. In the present invention, structure of the plasma generation section 14 is not particularly limited. Any suitable means may be used in addition to the so-called parallel flat-plates type. For example, the means includes electron cyclotron resonance (ECR) type, helicon wave plasma (HWP) type, inductively coupled plasma (ICP) type or a monopole antenna type plasma generation means which is described in e.g., Japan Laid-open Patent Publication No. JP-A-2003-86581 regarding a patent application of the present applicant.

FIG. 2 is an example of a diagram for illustrating a variety of states of the atoms of the helium gas in the plasma P to be generated in the interior of the reaction container 12 by the plasma generation section 14. The atoms of the helium gas exist in the plasma in a variety of states including e.g., a ground state 1¹S₀ (S₀ in the figure), the first metastable state 2¹ S₀, the second metastable state 2³S₁, the first excited state 4³D, the second excited state 3³D and post-emission stable state 2³P⁰. Moreover, transitions t₁, t₂, t₃, t₄, t₅, t₆, s₁, and s₂ is occurred in the plasma. The transition t₁, is a transition from the ground state 1¹S₀ to the first excited state 4³D. The transition t₂ is a transition from the ground state 1¹S₀ to the second excited state 3³D. The transition t₃ is a transition from the first metastable state 2¹S₀ to the first excited state 4³D. The transition t₄ is a transition from the first metastable state 2¹S₀ to the second excited state 3³D. The transition t₅ is a transition from the second metastable state 2³S₁, to the first excited state 4³D. The transition t₆ is a transition from the second metastable state 2³S₁, to the second excited state 3³D. The transition s₁, is a transition from the first excited state 4³D to the post-emission state 2³P⁰. The transition s₂ is a transition from the second excited state 3³D to the post-emission state 2³P⁰. Processes in the transitions t₁, through t₆ are hereinafter referred to as excitation processes t₁, through t₆, whereas processes in the transitions s₁, and s₂ are hereinafter referred to as lower level transition processes s₁, and s₂. In the actual plasma, atoms in plasma state exist in other states besides the states illustrated in FIG. 2. Some transition processes, not described above, are accordingly assumable. For example, states 4³S and 3³S may exist as the excited states. For simple explanation, the states and the transition processes illustrated in FIG. 2 are only considered in the following explanation. Additionally, when other excited states, other metastable states and other transitions are considered for the helium gas, plasma electron temperature can be similarly computed using the following means and methods.

A device for measuring plasma electron temperature which is provided in the plasma processing device 10, an example of the plasma processing device of the present invention, is further composed of a measurement unit 30 and an electron temperature measurement section 22 of the measurement control unit 20 in addition to the gas providing section 11 for providing the helium gas.

The measurement unit 30 includes a laser irradiation section 32, a light detection section 34 and a fluorescence and emission measurement section 36. The laser irradiation section 32 irradiates laser light L_(m) having predetermined wavelength in the interior of the chamber 12. The light detection section 34 receives the laser light L_(m), which has transmitted through the interior of the chamber 12, and converts the received light into an electric signal in accordance with intensity of the received light. The fluorescence and emission measurement section 36 observes both of intensity of induced fluorescence from the atoms in the metastable state in the plasma P and intensity of emission of the plasma P in irradiation of the laser light L_(m). The laser irradiation section 32 is composed of a laser light source 38, an emitted light adjustment section 42 and an irradiation area adjustment section 43, for instance. The laser light source 38 is a tunable laser. The emitted light adjustment section 42 is composed of a filter and a lens (not illustrated in the figure) for appropriately adjusting the laser light L_(m) emitted from the laser light source 38. The irradiation area adjustment section 43 is capable of changing an irradiation area in the plasma P, to which the laser light L_(m) is irradiated, by moving positions of the laser light source 38 and the emitted light adjustment section 42 along a direction of an X-Z plane in the figure. In the present embodiment, the irradiation area of the laser light L_(m) in the plasma P is a one-dimensional area illustrated with a dotted line L in FIG. 1 (Actually, the irradiation area includes a dimension in a radial direction of the laser light beam).

The laser irradiation section 32 irradiates the laser light L_(m) to the generated plasma P, the laser light L_(m) having suitable wavelength which enables to excite the atoms of the helium gas in the metastable state in the generated plasma P. For example, laser light having the wavelength of 501.6 nm is irradiated as laser light L₁ for exciting the atoms of the first metastable state 2¹S₀. On the other hand, laser light having the wavelength of 1083 nm is irradiated as laser light L₂ for exciting the atoms of the second metastable state 2³S₁. In the present embodiment, the laser irradiation section 32 is capable of irradiating two types of laser light having different wavelengths for exciting the helium atoms in two metastable states, respectively.

Components of the laser irradiation section 32 are not limited to a tunable dye laser for irradiating a variety of laser light having different wavelengths and the like. Alternatively, the laser irradiation section 32 may be composed of two tunable laser light sources (e.g., semiconductor lasers) for irradiating different types of laser light having different wavelengths.

The emitted light adjustment section 42 adjusts wavelength and intensity of the laser light L_(m) to desired conditions using a filter and .a lens. The laser light L_(m) is to be irradiated to the plasma P through the laser incident window 16 a. The irradiation area adjustment section 43 adjusts an irradiation area of the laser light L_(m), in the plasma P by moving positions of the laser light source 38 and the emitted light adjustment section 42 along the direction of the X-Z plane in the figure. The electron temperature measurement section 22 of the measurement control unit 20 controls irradiation timing of the laser light from the laser light source 38, wavelength and intensity of the laser light L_(m) to be irradiated to the plasma P, and positions of the laser light source 38 and the emitted light adjustment section 42 (i.e., the irradiation area of the laser light L_(m) in the plasma P). In other words, the irradiation area of the laser light L_(m), in the plasma P, and intensity I₀(_(m)) of each of a variety of laser light L_(m), are preliminarily given in the measurement control unit 20. The laser light L_(m) has different wavelengths enabling to excite the atoms in the m-th metastable state when the laser light L_(m) is emitted from the laser light source 38 and is irradiated to the plasma P . In addition to a suitable laser emission section (e.g., wavelength variable semiconductor laser), the laser light source 38 is herein preferably provided with a wavemeter, a spectrum analyzer and the like (not illustrated in the figure) for measuring wavelength of laser light to be emitted, obtaining a lasing state of the laser light to be emitted, obtaining wavelength sweeping width and the like.

The light detection section 34 is provided with a photoelectric conversion section 44, a received light adjustment section 46 and a received light position adjustment section 47, for instance. The photoelectric conversion section 44 is composed of a PIN photodiode, a phototransistor and the like. The received light adjustment section 46 is composed of a filter and a lens for allowing the photoelectric conversion section 44 to appropriately receive light. The received light position adjustment section 47 moves positions of the received light adjustment section 46 and the photoelectric conversion section 44 along the direction of the X-Z plane in the figure for allowing the received light adjustment section 46 and the photoelectric conversion section 44 to appropriately receive the laser light L_(m). When the helium atoms in the m-th metastable state are excited by the laser light L_(m) to be irradiated to the plasma P, energy of the laser light L_(m) is absorbed by the helium atoms of the metastable state. In the present embodiment, the light detection section 34 outputs an electric signal from the photoelectric conversion section 44 in accordance with intensity I_(t) of each of a variety of laser light L_(m) of different wavelengths which have transmitted through the plasma P,. The outputted electric signal is sent to the electron temperature measurement section 22 in the measurement control unit 20.

The fluorescence and emission measurement section 36 is provided with a CCD camera 48 and an observed light adjustment section 49 composed of a lens, a filter and the like. The observed light adjustment section 49 is composed of a lens unit (not illustrated in the figure), a plurality of filters (not illustrated in the figure) and a filter selection section (not illustrated in the figure), for instance. The lens unit guides light emitted from the entire plasma P generated in the interior of the reaction container 12 to a light receiver of the CCD camera 48. The filters are disposed in predetermined positions for selecting wavelength of incident light to a light receiving surface (i.e., a surface on which pixels are disposed) of the CCD camera 48. The filter selection section selects one of the filters and disposes the selected filter in a predetermined position. The selected filter covers the light receiving surface of the CCD camera 48 in the predetermined position. When the selected filter is disposed in the predetermined position, the selected filter only allows light having specific wavelength to transmit through it and enter the light receiving surface of the CCD camera 48. In the present embodiment, four types of filters are prepared. Light, allowed to transmit through each of four filters, has different wavelength from each other. For example, the first filter allows fluorescence having wavelength of 501.6 nm to transmit through it. In this case, the fluorescence corresponds to first induced fluorescence, generated when the atoms in the first metastable state 2¹S₀ is excited by the laser light L₁ (wavelength thereof is 501.6 nm). The second filter allows fluorescence having wavelength of 1083 nm to transmit through it. In this case, the fluorescence corresponds to second induced fluorescence, generated when the atoms in the second metastable state 2³S₁ is excited by the laser light L₂ (wavelength thereof is 1083 nm). Also, the third filter allows fluorescence having wavelength of 447 nm to transmit through it. In this case, the fluorescence corresponds to light emission in the lower level transition processes s₁. Also, the fourth filter allows fluorescence having wavelength of 588 nm to transmit through it. The fluorescence corresponds to light emission in the lower level transition processes s₂. The observation light adjustment section 49 is further provided with other filter-related component. The filter-related component herein blocks stray light of the laser light itself and a variety of noise light due to emission of plasma for reliably allowing each fluorescence and each emission to selectively pass through a corresponding one of the filters.

A lens unit (not illustrated in the figure) of the observed light adjustment section 49 guides fluorescence and emission from an area in the plasma P, corresponding to a predetermined observation plane in parallel to a Y-Z plane in the figure, to the light receiver of the CCD camera 48. The lens unit (not illustrated in the figure) is capable of changing the focal distance. The lens unit is capable of moving a position, along an X axis in the figure, of the predetermined observation plane in parallel to the Y-Z plane in the figure by changing the focal length. In other words, the light receiving surface (the surface on which pixels are aligned) of the CCD camera 48 receives light coming from the observation plane in the plasma P (the predetermined observation plane in parallel to the Y-Z plane in the figure), while the observation plane is defined in accordance with the focal length of the lens unit (not illustrated in the figure) of the observed light adjustment section 49. As described above, a selected one of the filters selects light having predetermined wavelength. Accordingly, the light coming from the observation plane has wavelength selected by the selected filter and only a predetermined type of fluorescence or emission which has wavelength corresponding to the selected filter is allowed to enter the light-receiving surface of the CCD camera 48.

The CCD camera 48 outputs an electric signal, corresponding to intensity of light received for each of the pixels as two-dimensional intensity distribution data (image data of light intensity distribution) while associating the electric signal with a position of each of the pixels. In other words, the CCD camera 48 measures the light intensity data of fluorescence or emission, which has predetermined wavelength corresponding to a selected filter, with respect to each of observation points on the observation plane (a point corresponding to a position corresponding to each of the pixels of the CCD camera 48) defined by the focal length of the lens unit, and outputs two-dimensional light intensity distribution data of fluorescence or emission having the predetermined wavelength corresponding to the selected filter.

Light emission in the lower level transition process s₁ (light emission of 447 nm) and light emission in the lower level transition process s₂ (light emission of 588 nm) occur all over the plasma P. The CCD camera 48 is capable of outputting, by changing the focal length of the lens unit, the two-dimensional light intensity distribution data of emission in each of the lower level transition processes s₁ and s₂ on each of a plurality of observation planes which is disposed along the X-axis in the figure. In other words, the fluorescence and emission measurement section 36 is capable of obtaining spatial distribution data of intensity of emission in each of the lower level transition processes s₁ and s₂ in the XYZ space in the figure by variously changing the focal position of the lens unit.

Moreover, in the present embodiment, laser light irradiation area of each of the laser light L₁ for exciting the atoms in the first metastable state and the laser light L₂ for exciting the atoms in the second metastable state is one-dimensional area. As described below, the CCD camera 48 sets a position of each of the observation planes to be a position corresponding to each of a plurality of laser light irradiation areas. Then, the CCD camera 48 measures light intensity distribution data (i.e., one-dimensional light intensity distribution data) in each of the laser light irradiation areas regarding induced fluorescence generated when the atoms are excited by the laser light L_(m). The laser light irradiation area can be arbitrarily set along the Z-X plane in the figure. When each induced fluorescence intensity distribution is measured in the laser light irradiation area, the position of the observation plane (i.e., focal length of the lens unit) is set to a position corresponding to the laser light irradiation area. Thus, the fluorescence and emission measurement section 36 measures intensity distribution of each induced fluorescence in each of a plurality of laser light irradiation areas to be set (changed) along the Z-X plane, and thereby spatial distribution data of intensity of each induced fluorescence in the XYZ space in the figure can be obtained. When light emission (i.e., emission of 447 nm) in the lower level transition process s₁ and light emission (i.e., emission of 588 nm) in the lower level transition process s₂ are measured, the position of each of the observation planes is also set to be a position corresponding to each of the laser light irradiation areas. Accordingly, the fluorescence and light emission measurement section 36 obtains information of the first induced fluorescence, the second induced fluorescence, light emission (emission of 447 nm) in the lower level transition process s₁ and light emission (emission of 588 nm) in the lower level transition process s₂ for each of the observation points on each of the observation planes (a point corresponding to a position corresponding to each of the pixels of the CCD camera 48). Thus, the fluorescence and light emission measurement section 36 can output spatial distribution information in the plasma P regarding light having wavelength which corresponds to wavelength of light allowed to pass through the filter disposed in the predetermined position. Another example of the CCD camera for obtaining light intensity distribution data of emission from the plasma P is described in the aforementioned Japan Laid-open Patent Publication No. H10-83893, for instance. The outputted light intensity distribution data is sent to the electron temperature measurement section 22 of the measurement and control unit 20.

FIG. 3 is a schematic diagram for illustrating configuration of the measurement control unit 20. The measurement control unit 20 is composed of an electron temperature measurement section 22, a processing control section 24 and a plasma control section 26. The measurement control unit 20 is composed of a heretofore known computer, provided with the memory 21, the CPU 23, and input and output ports and data bus (not illustrated in the figure). The measurement control unit 20 sends/receives data to/from an external device through the data bus and the input and output ports (not illustrated in the figure), and the CPU 23 executes a program stored in the memory 21. Components of the measurement control unit 20, illustrated in FIG. 3, thereby work. Each of the components of the measurement control unit 20, illustrated in FIG. 3, may be formed in a dedicated circuit. The memory 21 of the measurement control unit 20 stores a variety of information to be described (e.g., l, n₀, A^(A) and A^(B), A_(i) ^(A) and A_(i) ^(B), and σ^(a) _(exb) to be described) used for computation of electron temperature as data base. Additionally, the measurement control unit 20 is connected to input means (not illustrated in the figure) composed of a keyboard, a mouse and the like. The measurement control unit 20 may control plasma processing and an operation for measuring electron temperature, in response to instructions of a condition or an execution which is externally inputted by an operator through the input means.

The processing control section 24 is a section for controlling operations of the entire plasma processing in the plasma processing device 10. The plasma control section 26 is also connected to the gas providing section 11, a vacuum pump (not illustrated in the figure), a pressure sensor (not illustrated in the figure) and the like. For example, the plasma control section 26 controls operations of the gas providing section 11 and the vacuum pump (not illustrated in the figure) based on pressure in the interior of the reaction container measured by the pressure sensor for maintaining atmosphere in the interior of the reaction container in a predetermined condition. Moreover, the processing control section 24 is connected to the plasma control section 26. The processing control section 24 regulates high-frequency voltage which is outputted from the plasma control section 26, and controls operations for measuring plasma electron temperature in the electron temperature measurement section 22.

The electron temperature measurement section 22 of the measurement control unit 20 includes a laser control section 52, a transmitted light intensity obtainment section 54 and fluorescence intensity and emission intensity obtainment section 60. The laser control section 52 controls emission of laser light from the aforementioned laser light source 38, wavelength and intensity of laser light to be emitted, and a laser light irradiation area. The transmitted light intensity obtainment section 54 receives an electric signal outputted from the light detection section 34 in accordance with intensity I_(t) of the laser light L_(m) which has transmitted through the plasma P. The fluorescence intensity and emission intensity obtainment section 60 (hereinafter simply referred to as “light intensity obtainment section 60”) obtains two-dimensional light intensity distribution data for each of various types of lights, which has wavelength corresponding to each of the filters and is outputted from the CCD camera 48. Examples of the various types of lights include: light having wavelength of 501.6 nm corresponding to the first induced fluorescence; light having wavelength of 1083 nm corresponding to the second induced fluorescence; light having wavelength of 447 nm corresponding to emission in the lower level transition process s_(i); and light having wavelength of 588 nm corresponding to emission in the lower level transition process S₂.

The laser control section 52 is connected to the processing control section 24. The processing control section 24 sends an instruction for irradiating laser light to the laser control section 52 under the condition that the plasma P is generated in the interior of the reaction container 12. In response to the instruction from the processing control section 24, the laser control section 52 controls operations of the irradiation area adjustment section 43, the laser light source 38 and the emitted light adjustment section 42 for emitting laser light having instructed wavelength and instructed intensity to a laser light irradiation area in response to the instruction. In the present embodiment, the laser control section 52 controls a corresponding component to irradiate laser light to each of a plurality of preliminarily-set laser light irradiation areas, which are instructed through an operator's external input and are stored in the memory 21, for instance. The laser control section 52 controls the laser light source 38 to irradiate, for instance, laser light having wavelength of 501.6 nm as the laser light L₁ for exciting the atoms of the first metastable state 2¹S₀ to each of the laser light irradiation areas. Subsequently, the laser control section 52 causes the laser light source 38 to irradiate, for instance, laser light having wavelength of 1083 nm as the laser light L₁ for exciting the atoms of the second metastable state 2³S₁ to each of the laser light irradiation areas

The electron temperature measurement section 22 further includes a transmittance derivation section 56, a metastable-state density distribution computation section 58 and an electron temperature computation section 62. The transmittance derivation section 56 obtains intensity I₀ of the laser light L_(m) to be irradiated to the plasma P, and intensity I_(t) of the laser light L_(m) that has transmitted through the plasma P. The intensity I_(t) has been obtained by the transmitted light intensity obtainment section 54. Based on the obtained intensities, the transmittance derivation section 56 computes transmittance I_(t)/I_(0(m)) of the laser light L_(m) in a laser light irradiation area in the plasma P. As described above, the laser irradiation section 32 sequentially irradiates the laser light L_(m) for exciting the atoms in the m-th metastable state to a plurality of laser light irradiation areas. The transmittance derivation section 56 computes information of the transmittance I_(t)/I_(0(m)) of each laser light L_(m) with respect to each of the plurality of the laser light irradiation areas. As described above, the laser irradiation section 32 emits the laser light L_(m) having wavelength and intensity in response to the instruction from the laser control section 52. When transmittance is computed, the transmittance derivation section 56 receives information of the intensity I₀ of the laser light L_(m) to be irradiated to the plasma P from the processing control section 24. The information of the transmittance I_(t)/I_(0(m)), computed by the transmittance derivation section 56, is sent to the metastable-state density distribution computation section 58.

The light intensity obtainment section 60 obtains information obtained and outputted by the aforementioned fluorescence and emission measurement section 36. The information herein represents distribution of induced fluorescence, generated when the atoms in the m-th metastable state is excited by the aforementioned laser light L_(m), in each of the laser light irradiation areas in the plasma P. The light intensity obtainment section 60 sends the obtained information representing distribution of induced fluorescence in each of the laser light irradiation areas to the metastable-state density distribution computation section 58.

The metastable-state density distribution computation section 58 computes density of the atoms of the helium gas in the first metastable state 2¹S₀ and density n₂ of the atoms of the helium gas in the second metastable state 2³S₁ in each of the laser light irradiation areas in the plasma P, by using information of the transmittance I_(t)/I_(0(m)) of the laser light L_(m) of each wavelength which has been sent from the transmittance derivation section 56. Detailed computation processing, executed by the metastable-state density computation section 58, will be hereinafter explained. Additionally, the metastable-state density distribution computation section 58 computes spatial distribution of density of the atoms in the first metastable state in each of the laser light irradiation areas, based on the computed density n₁ of the atoms in the first metastable state in each of the laser light irradiation areas and the information representing distribution of the first induced fluorescence in each of the laser light irradiation areas. Similarly, the metastable-state density distribution computation section 58 computes spatial distribution of density of the atoms in the second metastable state in each of the laser light irradiation areas, based on the computed density n₂ of the atoms in the second metastable state and the information representing distribution of the second induced fluorescence. In other words, absolute value of density of the atoms in each of the metastable states in each of a plurality of laser irradiation areas, which is to be set (changed) along the Z-X plane, is computed for each of the observation points in the plasma P. Based on this, a spatial distribution of the absolute value of the density of the atoms in each of the metastable states is derived. Detailed processing, executed by the metastable-state density distribution computation section 58, will be hereinafter explained. As described above, each of the observation points in the plasma P corresponds to a position of each of the pixels of the CCD camera 48 on the observation plane which is set in accordance with each of the irradiation areas of the laser light.

The electron temperature computation section 62 computes information of spatial distribution of electron temperature in the plasma P, using emission intensities of light having respective wavelengths (i.e., light having wavelength of 447 nm corresponding to emission in the lower level transition process s₁ and light having wavelength of 588 nm corresponding to emission in the lower level transition process S₂) and spatial distribution of the absolute value of density in each of the metastable states. The emission intensities is sent from the emission intensity obtainment section 60 and the spatial distribution is sent from the metastable-state density distribution computation section 58. As described above, the emission intensity obtainment section 60 receives, from the CCD camera 48, the two-dimensional light intensity distribution data of light having wavelength of 447 nm corresponding to emission in the lower level transition process s₁ and that of light having wavelength of 588 nm corresponding to emission in the lower level transition process s₂, both of the distribution data being computed on each of a plurality of the observation planes.

The electron temperature computation section 62 computes emission intensity ratio I_(A)/I_(B) for each of the observation points in the plasma P. The emission intensity ratio I_(A)/I_(B) is ratio of intensity (i.e., emission intensity) I_(A) of light having wavelength of 447 nm corresponding to emission in the lower level transition process s₁ to intensity (i.e., emission intensity) I_(B) of light having wavelength of 588 nm corresponding to light emission in the lower level transition process S₂. Thus, the absolute value of density of the atoms in the first metastable state, the absolute value of density of the atoms in the second metastable state, and the emission intensity ratio I_(A)/I_(B) are computed for each of the observation points in the plasma P.

The electron temperature computation section 62 computes electron temperature data for each of the observation points in the plasma P using the emission intensity ratio I_(A)/I_(B), which is computed as described above for each of the observation points in the plasma P, and the density n₁ of the atoms in the first metastable state 2¹S₀ and the density n₂ of the atoms in the second metastable state 2³S₁, both of which are computed by the metastable-state density distribution computation section 58. As described above, the electron temperature computation section 62 obtains data representing electron temperature for each of the observation points in the plasma P, that is, data representing spatial distribution of electron temperature in the plasma P. Detailed computation processing, executed by the electron temperature computation section 62, will be hereinafter explained.

The data representing the spatial distribution of electron temperature in the plasma P which is obtained by the electron temperature computation section 62, is sent to the processing control section 24. The processing control section 24 compares a preliminarily-set spatial distribution condition of electron temperature (base electron temperature condition) for allowing a desired plasma processing to be executed, and the spatial distribution data of electron temperature in the plasma P which is sent from the electron temperature computation section 62. In response to a result of the comparison, the processing control section 24 controls operations of the plasma control section 26, the gas providing section 11 and a vacuum pump (not illustrated in the figure) for generating the plasma P which satisfies a base electron temperature distribution condition. For example, the plasma control section 26 regulates high-frequency voltage to be provided to the plasma providing section 14 and the gas pressure in the interior of the reaction container 12, for instance, in response to the plasma regulation instruction which is sent from the processing control section 24. The plasma processing device 10 is configured as described above.

An example of a method of measuring plasma electron temperature of the present invention, executed by the plasma processing device 10, will be hereinafter explained. FIG. 4 is a flowchart of an example of the plasma processing to be executed by the plasma processing device 10. In the flowchart illustrated in FIG. 4, an example of a measurement of plasma electron temperature of the present invention is made together with the plasma processing.

First, under the control of the processing control section 24 of the measurement control unit 20, processing gas and helium gas are provided into the reaction container 12. Plasma P is accordingly generated in the interior of the reaction container 12 (Step S102). Specifically, the processing control section 24 controls the gas providing section 11 for providing predetermined processing gas and helium gas into the reaction container while controlling the vacuum pump (not illustrated in the figure) and the like to maintain pressure in the interior of the reaction container 12 at a predetermined vacuum level. Accordingly, the reaction container 12 is maintained to have ambient gas satisfying a predetermined condition. Under the control of the ambient gas in the reaction container 12 at the predetermined condition, the processing control section 24 instructs the plasma control section 26 to output high-frequency voltage. Thereby, plasma generation section 14 generates the plasma P in the interior of the reaction container 12. The plasma processing device 10 generates relatively stable plasma P for executing a variety of processing such as film formation and etching on the processing target substrate.

Next, the processing control section 24 sends an instruction for setting a laser light irradiation area to the laser control section 52. The laser control section 52 controls operations of the irradiation area adjustment section 43 for adjusting positions of the laser light source 38, the emitted light adjustment section 42, the photoelectric conversion section 44 and the received light adjustment section 46 (Step S 104). Under the above adjusted state, the processing control section 24 sends an instruction for emitting laser light to the laser control section 52. The laser control section 52 accordingly causes a corresponding component to emit laser light having wavelength and intensity in accordance with the instruction from the processing control section 24, thereby irradiating laser light L_(m) to the generated plasma P (Step S106). In the present embodiment, the laser control section 52 control the laser light source 38 to emit laser light L₁ having wavelength of 501.6 nm, for instance, as laser light for exciting the atoms in the first metastable state 2¹S₀, for the purpose of irradiating the plasma P. Subsequently, the laser control section 52 controls the laser light source 38 to emit laser light L₂ having wavelength of 1083 nm, for instance, as laser light for exciting the atoms in the second metastable state 2 ³S₁, for the purpose of irradiating the plasma P (Step S106).

When the laser light L_(m) of each of two wavelengths is irradiated, the transmittance derivation section 56 obtains intensity I₀ of the laser light L_(m) to be irradiated to the plasma P and intensity I_(t) of the laser light L_(m) which has transmitted through the plasma P and is obtained by the transmitted light intensity obtainment section 54, for the laser light L_(m) having each of the wavelengths for exciting the atoms in the m-th metastable state. Subsequently, the transmittance derivation section 56 derives transmittance I_(t)/I_(0(m)) of the laser light L_(m) in the present laser light irradiation area in the plasma P for the laser light having each of the wavelengths (Step S108). In other words, the transmittance derivation section 56 computes transmittance I_(t)/I₀₍₁₎ in the present laser light irradiation area when the laser light L₁ for exciting the atoms in the first metastable state 2¹S₀ is irradiated, and transmittance I_(t)/I₀₍₂₎ in the present laser light irradiation area when the laser light L₂ for exciting the atoms in the second metastable state 2³S₁ is irradiated, respectively. Transmittance of each of the laser light L_(m) in the present laser light irradiation area is sent to the metastable-state density distribution computation section 58.

The metastable-state density distribution computation section 58 computes the absolute value n₁ of density of the atoms in the first metastable state 2¹S₀ in the present laser light irradiation area and the absolute value n₂ of density of the atoms in the second metastable state 2³S₁ in the present laser light irradiation area, respectively, using transmittance information I_(t)/I_(0(m)) of the laser light L_(m) which has each of the wavelengths in the present laser light irradiation area and is sent from the transmittance derivation section 56 (Step S110). The metastable-state density distribution computation section 58 computes the absolute value n₁ of density of the atoms in the first metastable state 2¹S₀ based on the transmittance I_(t)/I₀₍₁₎ derived when the laser light L₁ for exciting the atoms in the first metastable state 2¹S₀ is irradiated. Additionally, the metastable-state density computation section 58 computes the absolute value n₂ of density of the atoms in the second metastable state 2³S₁ based on the transmittance I_(t)/I₀₍₂₎ derived when the laser light L₂ for exciting the atoms in the second metastable state 2³S₁ is irradiated.

More specifically, density of the helium gas atoms in each of the first and second metastable states in the plasma P is computed using the following generalized formula (3).

$\begin{matrix} \left\lbrack {{Formula}\mspace{14mu} 4} \right\rbrack & \; \\ {\frac{I_{t}}{I_{0{(m)}}} = {\exp\left\{ {{- {\sigma_{exm}(v)}}n_{m}1} \right\}}} & (3) \end{matrix}$

In the formula (3), “n_(m) (m=1,2)” represents the absolute value of density to be computed. Additionally, “σ_(exm)(v)” represents absorption cross section of the atoms in the m-th metastable state in absorbing light having wavelength v. Moreover, “l” represents length of the transmitting path of the laser light in the plasma P (absorption length). A memory (not illustrated in the figure) of the measurement control unit 20 preliminarily stores value of “l”. The metastable-state density distribution computation section 58 reads out the value “l” stored in the memory, and uses it. Furthermore, the absorption cross section σ_(exm)(v) of the atoms in the m-th metastable state is computed using the following formula (4) wherein center wavelength of the irradiated laser light (more specifically, center wavelength of light absorbed by the helium atoms in the m-th metastable state) v=v₀.

$\begin{matrix} \left\lbrack {{Formula}\mspace{14mu} 5} \right\rbrack & \; \\ {{\sigma_{exm}\left( v_{0} \right)} = {\frac{h\; v_{0}B_{12}}{c}\frac{1}{\Delta\; v_{d}}\sqrt{\frac{\ln\; 2}{\pi}}}} & (4) \end{matrix}$

In the formula (4), “h” represents Planck's constant; “B₁₂” represents Einstein B-coefficient; “c” represents velocity of light; and “Δν_(d)” represents Doppler width. For “Δν_(d)” in the formula (4), the following formula (5) is derived which represents relation with temperature T of the helium atoms in the metastable state. In the formula (5), “M” represents mass of one Helium atom, whereas “k” represents Boltzmann constant.

$\begin{matrix} \left\lbrack {{Formula}\mspace{20mu} 6}\; \right\rbrack & \; \\ {{\Delta\; v_{d}} = {v_{0}\sqrt{\ln\; 2}\sqrt{\frac{2\;{kT}}{{Mc}^{2}}}}} & (5) \end{matrix}$

Note temperature T of the helium atoms in the metastable state can be easily computed using a variety of heretofore known methods in the field of the present invention (e.g., absorption spectrum width). In the plasma processing device 10 illustrated in FIG. 1, for instance, temperature T of the helium atoms can be computed by sweeping wavelength of the laser light L_(m) to be irradiated in the interior of the reaction container 12 and measuring a shape of absorption spectrum broadened by Doppler effect due to thermal motion of the helium atoms, for instance, using a spectrum analyzer (not illustrated in the figure). Additionally, value of temperature T of the helium atoms herein used may be preliminarily stored in the memory (not illustrated in the figure) of the measurement and control unit 20.

When the formulas (3) to (5) are integrated, density n_(m) of the helium atoms in the m-th metastablle state in irradiating laser light having wavelength v_(O) (note width of the wavelength of laser light is herein negligible) can be expressed by the following formula (6). The metastable-state density distribution computation section 58 computes density n_(m)of the helium atoms in the m-th metastable state using the formula (6), for instance. In the present embodiment, for instance, density n₁ of the atoms in the first metastable state 2¹S₀ and density n₂ of the atoms in the second metastable state 2³S₁ are computed respectively. The computed density n₁ and density n₂ of the atoms in each of the above metastable states are sent to the electron temperature computation section 62.

$\begin{matrix} \left\lbrack {{Formula}\mspace{20mu} 7} \right\rbrack & \; \\ {n_{m} = {- \frac{\ln\mspace{11mu}{I_{1}/I_{0{(m)}}}}{{\sigma_{exm}\left( v_{0} \right)}1}}} & (6) \end{matrix}$

In addition to computation of density of the atoms in the metastable state in the present laser light irradiation area, the light intensity obtainment section 60 further obtains information representing a spatial distributions of each induced fluorescence generated when the atoms are excited by the laser light L_(m) (Step S112). As described above, a laser light irradiation area of the laser light L₁ for exciting the atoms in the first metastable state and that of the laser light L₂ for exciting the atoms in the second metastable state in a single laser light irradiation position are one-dimensional areas respectively. In Step S112, a position of the observation plane is set to be a position corresponding to a one-dimensional laser light irradiation area. Based on this, light intensity distribution data of induced fluorescences (first induced fluorescence and second induced fluorescence) generated when the atoms are excited by the laser light L_(m) in the laser light irradiation area (i.e., one-dimensional light intensity distribution data) is outputted as illustrated in FIG. 5, for instance. In FIG. 5, a horizontal axis Y represents a position in a direction Y illustrated in FIG. 1B. Information representing a spatial distribution of each induced fluorescence in the present laser light irradiation area (e.g., information illustrated in FIG. 5) is sent to the metastable-state density distribution computation section 58, the induced fluorescence being generated when the atoms are excited by the laser light L_(m).

The metastable-state density distribution computation section 58 derives spatial distribution of the absolute value of density of the atoms in the first metastable state 2¹S₀ in the present laser light irradiation area using information representing spatial distribution of the first induced fluorescence in the present laser light irradiation area obtained in Step S112 (e.g., information illustrated in FIG. 5) and the density n_(i) of the atoms in the first metastable state 2¹S₀ in the present laser light irradiation area obtained in Step S110 (Step S114). Similarly, spatial distribution of the absolute value of density of the atoms in the second metastable state in the present laser light irradiation area is derived using information representing spatial distribution of the second induced fluorescence in the present laser light irradiation area (e.g., information illustrated in FIG. 5) and the density n₂ of the atoms in the second metastable state in the present laser light irradiation area, obtained in Step S110. The absolute values n₁ and n₂ of density of the atoms in the metastable states, obtained in Step S110, represent average of respective densities in the present light irradiation area, respectively. On the other hand, information representing a spatial distribution of the first induced fluorescence, obtained in Step S112, represents not the absolute value of density, but a relative spatial distribution of density of the atoms in the first metastable state. Similarly, information representing a spatial distribution of the second induced fluorescence represents not the absolute value of density, but a relative spatial distribution of density of the atoms in the second meastable state. For example, a spatial distribution of each of the absolute values n₁ and n₂ of density of the atoms in each of the metastable states in the present laser light irradiation area can be computed (see FIG. 5), when an average intensity obtained in Step S112 of the induced fluorescence in the present laser light irradiation area is assumed to correspond to fluorescence intensity in the average density of the atoms in the metastable state in the laser light irradiation area, the average intensity being computed based on the information of representing a spatial distribution of each induced fluorescence. The computed spatial distribution of each of the absolute values n₁ and n₂ of density of atoms in each of the metastable states in a laser light irradiation area is stored in the memory (not illustrated in the figure), for instance.

Processing, executed in each of Steps S104 to S114, is repeated until a spatial distribution of each of the absolute values n₁ and n₂ of density of the atoms in each of the metastable states is derived in all the preliminarily-set laser irradiation areas, in other words, until a determination of Step S116 is “Yes” . Thus, spatial distribution of each of the absolute values n₁ and n₂ of density of the atoms in each of the metastable states in a plurality of laser light irradiation areas is derived, and thereby spatial distribution of each of the absolute values n₁ and n₂ of density of the atoms in the entire plasma P is derived in each of the metastable states.

Next, the fluorescence and emission measurement section 36 measures light emission generated in the lower level transition process s₁ and light emission generated in the lower level transition process s₂ in each of a plurality of observation planes corresponding to each of the laser light irradiation areas (Step S118). The emission intensity obtainment section 60 receives, from the CCD camera 48, two-dimensional light intensity distribution data which is measured for each of a plurality of the observation planes. The two-dimensional light intensity distribution data herein relates to each of light having wavelength of 447nm corresponding to light emission generated in the lower level transition process s₁ and light having wavelength of 588nm corresponding to light emission generated in the lower level transition process s₂. The electron temperature computation section 62 computes emission intensity ratio I_(A)/I_(B) for each of the observation points in the plasma P. The emission intensity ratio I_(A)/I_(B) is ratio of intensity (emission intensity) I_(A) of light having wavelength of 447nm corresponding to light emission generated in the lower level transition process s₁ to intensity (emission intensity) I_(B) of light having wavelength of 588 nm corresponding to light emission generated in the lower level transition process s₂. The emission intensity ratio I_(A)/I_(B) is computed for each of the observation points in the plasma P, and data for representing spatial distribution of the emission intensity ratio I_(A)/I_(B) is subsequently obtained (Step S120).

Next, the electron temperature computation section 62 computes a spatial distribution of electron temperature in the plasma P using: data representing spatial distribution of the emission intensity ratio I_(A)/I_(B) which is sent from the emission intensity obtainment section 60; and a spatial distribution of the absolute value n₁ of density of the atoms in the first metastable state 2¹S₀ and spatial distribution of the absolute value n₂ of density of the atoms in the second metastable state 2³S₁, both of which are sent from the metastable-state density computation section 58 (Step S122). To make the explanation simpler and easier, the following relates to a case that electron temperature, corresponding emission intensity ratio for one of the observation points (i.e., in a single position in the plasma P), is computed based on the emission intensity ratio I_(A)/I_(B) for the observation point and the absolute values n₁ and n₂ of density of the atoms in the metastable states corresponding to the observation point. As described above, the emission intensity ratio I_(A)/I_(B) and the absolute values n₁ and n₂ of density of the atoms in the metastable states are given for each of the observation points, and electron temperature for each of the observation points can be computed using the following method.

The following formula (7) expresses a rate equation for determining the helium atoms in the first excited state 4³D (hereinafter referred to as “first excited state A”) in the plasma P.

$\begin{matrix} \left\lbrack {{Formula}\mspace{14mu} 8} \right\rbrack & \; \\ {\frac{\mathbb{d}n_{A}^{*}}{\mathbb{d}t} = {{k_{{ex}\; 0}^{A}n_{0}n_{e}} + {k_{{ex}\; 1}^{A}n_{1}n_{e}} + {k_{{ex}\; 2}^{A}n_{2}n_{e}} - {A^{A}n_{A}^{*}}}} & (7) \end{matrix}$

In the formula, “n_(A) ^(*)” represents density of the atoms in the first excited state A; “k^(A) _(ex0)” represents an electron impact excitation rate constant in an excitation process t₁; “n₀” represents density of the atoms in a ground state; “n_(e)” represents electron density; “k^(A) _(ex1)” represents an electron impact excitation rate constant of an excitation process t₃; “n₁” represents the computed density of the atoms in the first metastable state; “k^(A) _(ex2)” represents an electron impact excitation rate constant of an excitation process t₅; “n₂” represents the computed density of the atoms in the second metastable state; and “A^(A)” represents inverse of a radiative lifetime of the atoms in the first excited state A.

Similarly, the following formula (8) expresses a rate equation for determining the helium atoms in the second excited state 3³D (hereinafter referred to as “second excited state B”) in the plasma P.

$\begin{matrix} \left\lbrack {{Formula}\mspace{14mu} 9} \right\rbrack & \; \\ {\frac{\mathbb{d}n_{B}^{*}}{\mathbb{d}t} = {{k_{{ex}\; 0}^{B}n_{0}n_{e}} + {k_{{ex}\; 1}^{B}n_{1}n_{e}} + {k_{{ex}\; 2}^{B}n_{2}n_{e}} - {A^{B}n_{B}^{*}}}} & (8) \end{matrix}$

In the formula, “n_(B) ^(*)” represents density of the atoms in the second excited state B; “k^(B) _(ex0)” represents an electron impact excitation rate constant in an excitation process t₂; “k^(B) _(ex1)” represents an electron impact excitation rate constant in an excitation process t₄; “k^(B) _(ex2)” represents an electron impact excitation rate constant in an excitation process t₆; and “A^(B)” represents inverse of a radiative lifetime of the atoms in the second excited state B. The density n₀ of the atoms in a ground state, the electron density n_(e),the computed density n₁ of the atoms in the first metastable state and the computed density n₂ of the atoms in the second metastable state are obviously shared by the formulas (7) and (8). Additionally, “n_(A) ^(*)” in the formula (7) corresponds to an intensity of light emission generated in the lower level transition process S₁ whereas “n_(B) ^(*)” in the formula (8) corresponds to an intensity of light emission generated in the lower level transition process s₂.

When the plasma P is in a steady state, values of the both sides of the rate equations (7) and (8) are zero. When ratio of the formula (7) to the formula (8) is computed and relation of emission intensity ratio I_(A)/I_(B) is organized, the following relation equations (1) are obtained.

$\begin{matrix} \left\lbrack {{Formula}\mspace{14mu} 10} \right\rbrack & \; \\ \left. \begin{matrix} {\frac{{k_{{ex}\; C}^{A}n_{C}} + {\sum\limits_{m = 1}{k_{exm}^{A}n_{m}}}}{{k_{{ex}\; C}^{B}n_{C}} + {\sum\limits_{m = 1}{k_{exm}^{B}n_{m}}}} = {\frac{A^{A}}{A^{B}} \cdot \frac{n_{A}^{*}}{n_{B}^{*}}}} \\ {\frac{I_{A}}{I_{B}} = {\frac{g^{A}}{g^{B}} \cdot \frac{\lambda^{B}}{\lambda^{A}} \cdot \frac{A_{i}^{A} \cdot n_{A}^{*}}{A_{i}^{B} \cdot n_{B}^{*}}}} \end{matrix} \right\} & (1) \end{matrix}$

In the formula (1), “A_(i) ^(A)” represents an Einstein A-coefficient of light emission generated in the lower level transition process S₁ of the atoms in the first excited state A, whereas “A_(i) ^(B)” represents an Einstein A-coefficient of light emission generated in the lower level transition process s₂ of the atoms in the second excited state B. As heretofore known, A^(A) which is inverse of radiative lifetime of the atoms in the first excited state A is a value represented by the sum of Einstein A-coefficients in a plurality of natural transition processes (i.e., a transition process s_(i) and the like) of the atoms in the first excited state A. On the other hand, A^(B) which is inverse of a radiative lifetime of the atoms in the second excited state B is a value represented by the sum of Einstein A-coefficients in a plurality of natural transition processes (i.e., a transition process s₂) of the atoms in the second excited state B. Additionally, “n_(m)” represents the computed density of the atoms in the m-th metastable state; “k^(A) _(exm)” represents an electron impact excitation rate constant from the m-th metastable state to the first excited stable state A; and “k^(B) _(exm)” represents an electron impact excitation rate constant from the m-th metastable state to the second excited stable state B. Moreover, “k^(A) _(ex0),” “k^(A) _(exm),” “k^(B) _(ex0)” and “k^(B) _(exm)” are functions of electron temperature. Also, “g^(A), g^(B)” is a function of wavelength σ^(A), σ^(B), and represent solid angle and quantum efficiency of the observation system in the excited states A and B. Here, σ^(A), σ^(B) is wavelength of light to be measured in the excited states A and B.

Note the density n₀ of the atoms in the ground state is determined by the gas pressure. Database of the density n₀ on gas pressure basis is preliminarily stored in the memory (not illustrated in the figure) of the measurement control unit 20. Additionally, the A^(A) which is inverse of a radiative lifetime of the atoms in the first excited state A, the Einstein A-coefficient A_(i) ^(A) in the transition process s₁ from the first excited state A to a lower level, the A^(B) which is inverse of a radiative lifetime of the atoms in the second excited state B, the Einstein A-coefficient A_(i) ^(B) in the transition process s₂ from the second excited state B to a lower level, the coefficients g^(A), g^(B) and the wavelengths σ^(A), σ^(B) are not particularly influenced by other parameters, and are preliminarily stored as database in the memory (not illustrated in the figure) of the measurement control unit 20.

Additionally, the following formula (2) represents the rate constant k^(a) _(exb) (note a character “A” or “B” which represents an excited state is generalized as a character “a”, whereas a numeral “0” or a character “m” which represents a state of the atoms is generalized as a character “b”). [Formula 11] k _(exb) ^(a)=∫νσ_(exb)(ν)f(ν)dν  (2)

In the above formula (2), “σ_(exb)” is cross section in respective excitation processes. Therefore, “σ_(exb)” will be hereinafter referred to as “σ^(a) _(exb)”(“a” represents the character “A” or “B” that represents an excitation state). Additionally, “σ^(a) _(exb)” represents cross section in respective excitation processes; “v” represents electron velocity; and “f(v)” represents an electron energy distribution function. In this case, each of “σ^(a) _(exb), ” “v,” and “f(v)” is a function of electron temperature T_(e) of the plasma P, and is heretofore known. Specifically, “σ^(a) _(exb)” is known as described in a heretofore known conventional document (e.g., “Cross Section Database for Collision Processes of Helium Atom with Charged Particles” by Yu. V. Ralchenko, R. K. Janev, T. Kato, D. V. Fursa, I. Bray and F. J. de Heer, National Institute for Fusion Science “NTFS-DATA-59,” Oct. 2000). Also, “σ^(a) _(exb)” is stored, for instance as database, in the memory (not illustrated in the figure) of the measurement control unit 20. The helium gas to be used in the present invention has relatively simple atomic structure. A great deal of information (e.g., cross section in an excitation process) is accurately known. In the present invention, at least the helium gas is mixed with the processing gas, and electron temperature is computed using plasma of the helium gas. Therefore, plasma electron temperature can be computed with relatively high accuracy using a relatively simple device configuration.

The plasma electron temperature computation section 62 solves an equation expressed only by a function of the plasma electron temperature T_(e) to compute a value of plasma electron temperature T_(e). The equation is herein obtained by substituting the following into the above formulas (1) and (2): the emission intensity ratio I_(A)/I_(B); the computed density n_(m) of the atoms in the m-th metastable state; n₀ to be determined in accordance with the gas pressure preliminarily stored in the memory (not illustrated in the figure); the A^(A) and the A^(B) which are determined by an excitation level; the Einstein A-coefficients A_(i) ^(A) and A_(i) ^(B) in accordance with respective transition processes; and the σ^(a) _(exb), v and f(v) preliminarily stored in the memory (not illustrated in the figure). The present invention is one of features that plasma electron temperature is computed based on the rate equation derived in consideration of both an excitation state and a metastable state of the atoms in the plasma.

The electron temperature computation section 62 computes data of electron temperature of the plasma P for each position in the plasma P, and obtains data representing spatial distribution of electron temperature in the plasma P. The electron temperature computation section 62 sends data representing spatial distribution of electron temperature in the plasma P to the processing control section 24.

The processing control section 24 regulates, for instance, high-frequency voltage to be provided to the plasma generation section 14 in accordance with the data representing spatial distribution of electron temperature in the plasma P, thereby generating the plasma P which satisfies a base electron temperature distribution condition. The plasma P is thus regulated (Step S124). The plasma processing device 10 is configured as described above.

In the aforementioned embodiment, beam-shaped laser light is used as the laser light to be irradiated to the plasma. In the present invention, however, slit-shaped laser light which travels while broadening along a plane parallel to the Z-Y plane in the figure, may be used, for measuring the induced fluorescence intensity, as laser light to be irradiated to the plasma, for instance. In other words, simultaneous induced fluorescence may be generated in the entire observation plane by irradiating the laser light so that the laser light irradiates the entire observation plane at a time while traveling entirely within the observation plane. In this case, when the laser light is irradiated to an observation plane once, two-dimensional distribution information of induced fluorescence can be obtained by the CCD camera. Additionally, wavelength of laser light for generating induced fluorescence and wavelength of laser light for measuring transmittance may not necessarily be identical to each other, but may be different from each other. For example, the number of filters to be disposed on the light receiving surface of the CCD camera can be reduced by setting wavelength of laser light for generating induced fluorescence corresponding to the filters.

Moreover, in the aforementioned embodiment, an emission intensity ratio is computed by measuring light emission generated in the lower level transition process from the state 4³D (i.e., the first excited state) to the state 2³P⁰ and light emission generated in the lower level transition process from the state 3³D (i.e., the second excited state) to the state 2³P⁰. In the present invention, for instance, a ratio between light emission generated in a lower level transition process from the state 4³S to the state 2³P⁰ and light emission generated in a lower level transition process from the state 3³S to the state 2³P⁰ may be used as the emission intensity ratio. For example, light having wavelength of 471.6 nm may be measured as light emission generated in the lower level transition process from the state 4³S to the state 2³P⁰. On the other hand, light having wavelength of 706.5 nm may be measured as light emission generated in the lower level transition process from the state 3³S to the state 2³P⁰.

According to the present invention, plasma electron temperature can be computed based on both of density of the atoms in the metastable state in the plasma and density of the atoms in the excited state in the plasma using a relatively cheap measurement device having relatively simple stricture. According to the present invention, plasma electron temperature can be computed with relatively higher accuracy compared to the two conventional methods of computing plasma electron temperature, one of the methods being only based on density of the atoms in the metastable state, the other being only based on density of the atoms in the excited state. Furthermore, a spatial distribution of electron temperature of the generated plasma can be obtained with relatively high accuracy.

As described above, the method and device for measuring the plasma electron temperature have been described in detail. However, the present invention is not limited to the aforementioned embodiment. A variety of changes and modifications are obviously available for the aforementioned embodiment without departing from the scope of the present invention. 

1. A method of measuring electron temperature of generated plasma, comprising the steps of: providing at least helium gas to a predetermined container to generate plasma in the predetermined container; irradiating laser light, by using a laser irradiation device, to the generated plasma, the laser light having wavelength which is capable of exciting atoms of the helium gas in a metastable state, to excite the atoms in the metastable state; obtaining absorption amount information, by using a laser irradiation device, representing an amount of the laser light absorbed by the atoms in the metastable state; computing density of the atoms of the helium gas in the metastable state in an irradiation area of the laser light in the plasma based on the absorption amount information by using a computer; measuring each of light emissions, by using a camera, due to level transition processes from two different excited states of the helium gas in the plasma to a state having an energy level lower than an energy level of the excited states and computing an emission intensity ratio between the light emissions; and computing electron temperature of the generated plasma based on the emission intensity ratio and the computed density of the atoms of the helium gas in the metastable state by using the computer.
 2. The method of measuring plasma electron temperature according to claim 1, further comprising the steps of: irradiating laser light to the generated plasma, by using the laser irradiation device, the laser light having wavelength which is capable of exciting the atoms of the helium gas in the metastable state, to excite the atoms in the metastable state; and obtaining information of a distribution of induced fluorescence intensity, by the camera in the irradiation area along a path of the laser light, the induced fluorescence intensity representing intensity of induced fluorescence from the atoms in the metastable state, the induced fluorescence being caused by irradiation of the laser light, and wherein, in the step of computing density of the atoms in the metastable state, a distribution of density of the atoms in the metastable state in the irradiation area along the path of the laser light is at least computed based on the absorption amount information and the information of the distribution of the induced fluorescence intensity.
 3. The method of measuring plasma electron temperature according to claim 1, wherein, in the step of computing density of the atoms of the helium gas in the metastable state, density of the atoms in each of states 2¹S₀ and 2³S₁ is computed as the density of the atoms in the metastable states, and in the step of computing the emission intensity ratio, the emission intensity ratio is computed by measuring a light emission due to level transition processes from a state 4³D to a state 2³P⁰, corresponding to a wavelength of 447 nm and a light emission due to a level transition process from a state 3³D to the state 2³P⁰, corresponding to a wavelength of 588 nm.
 4. The method of measuring plasma electron temperature according to claim 1, wherein, in the step of the computing density of the atoms in the metastable state, density of the atoms in each of states 2¹S₀ and 2³S₁ is computed as the density of the atoms in the metastable state, and in the step of computing the emission intensity ratio, the emission intensity ratio is computed by measuring a light emission due to a level transition process from a state 4³S to a state 2³P⁰, corresponding to a wavelength of 471.6 nm, and a light emission due to a lower level transition process from a state 3³S to the state 2³P⁰, corresponding to a wavelength of
 706. 5nm.
 5. The method of measuring plasma electron temperature according to claim 1, wherein, in the step of computing the electron temperature, the plasma electron temperature is computed using the following formula (1), $\begin{matrix} \left. \begin{matrix} {\frac{{k_{{ex}\; 0}^{A}n_{0}} + {\sum\limits_{m = 1}{k_{exm}^{A}n_{m}}}}{{k_{{ex}\; 0}^{B}n_{0}} + {\sum\limits_{m = 1}{k_{exm}^{B}n_{m}}}} = {\frac{A^{A}}{A^{B}} \cdot \frac{n_{A}^{*}}{n_{B}^{*}}}} \\ {\frac{I_{A}}{I_{B}} = {\frac{g^{A}}{g^{B}} \cdot \frac{\lambda^{B}}{\lambda^{A}} \cdot \frac{A_{i}^{A} \cdot n_{A}^{*}}{A_{i}^{B} \cdot n_{B}^{*}}}} \end{matrix} \right\} & (1) \end{matrix}$ and wherein, in the formula (1), each of numerals relates to the atoms of the helium gas in the plasma; “I_(A)” represents a measured value of intensity of the light emission due to a lower level transition process from a first excited state A to a state having an energy level lower than an energy level of the first excited state A, whereas “I_(B)” represents a measured value of intensity of the light emission due to a level transition process from a second excited state B to a state having an energy level lower than an energy level of the second excited state B; “A_(i) ^(A)” represents an Einstein A-coefficient of the light emission due to the level transition process from the first excited state A to a state having an energy level lower than an energy level of the first excited state A, whereas “A_(i) ^(B)” represents an Einstein A-coefficient of the light emission due to the level transition process from the second excited state B to a state having an energy level lower than an energy level of the second excited state B; “A^(A)” represents an inverse of a radiative lifetime of the atoms in the first excited state A to a state having an energy level lower than an energy level of the first excited state A, which is represented by the sum of Einstein A-coefficients in a plurality of natural transition processes from the first excited state A, whereas “A^(B)” represents an inverse of a radiative lifetime of the atoms in the second excited state B, which is represented by the sum of Einstein A-coefficients in a plurality of natural transition processes from the second excited state B; “n_(m)” represent the computed density of the atoms in the m-th metastable state; “n₀” represents density of the atoms in a ground state; “n_(A) ^(*)” represents density of the atoms in the first excited state A; and “n_(B) ^(*)” represents density of the atoms in the second excited state B; “k^(A) _(ex0)” represents an electron impact excitation rate constant from the ground state to the first excited state A, whereas “k^(A) _(eXm)” represents an electron impact excitation rate constant from the m-th metastable state to the first excited state A; “k^(B) _(ex0)” represents an electron impact excitation rate constant from the ground state to the second excited state B, whereas “k^(B) _(exm)” represents an electron impact excitation rate constant from the m-th metastable state to the second excited state B, and “k^(A) _(ex0),” “k^(A) _(exm),” “k^(B) _(ex0)” and “k^(B) _(exm)” are functions of the plasma electron temperature; “g^(A), g^(B)” are functions of wavelengths λ^(A) and λ^(B), each representing solid angle and quantum efficiency of an observation system in each of the excited states A and B, and “λ^(A), λ^(B)” are wavelengths of light to be measured in the excited states A and B.
 6. The method of measuring plasma electron temperature according to claim 5, wherein the rate constant k^(a) _(exb) to be used in the step of computing the electron temperature is represented by the following formula (2) and the plasma electron temperature is computed using the formula (1), k _(exb) ^(a) =∫vσ _(exb)(v)f(v)dv  (2) and wherein, in the formula (2), “a” represents “A” or “B”, whereas “b” represents “0” or “m”; and “σ^(a) _(exb)” represents cross section in each of the excitation processes; “v” represents electron velocity; and “f(v)” represents an electron velocity distribution function.
 7. The method of measuring plasma electron temperature according to claim 1, wherein, in the step of obtaining the absorption amount information, transmittance of the laser light irradiated to the plasma is obtained as the absorption amount information representing the amount of absorption of the laser light.
 8. The method of measuring plasma electron temperature according to claim 7, wherein, in the step of obtaining the absorption amount information, transmittance I_(t)/I_(0(m)) of the laser light is computed by obtaining intensity I₀ of laser light to be irradiated to the plasma for exciting the atoms in the m-th metastable state and intensity I_(t) of the laser light which has transmitted through the plasma, in the step of computing the density of the atoms of the helium gas in the metastable state, density n_(m) of the atoms of the helium gas in the metastable state in the plasma is computed based on the transmittance I_(t)/I_(0(m)) of the laser light and the following formula (3), I_(t)/I_(0(m))=exp {−σ_(exm) (v) n_(cl)I}  (3) and wherein, in the formula (3), “σ_(exm)” represents absorption cross section of the atoms in the m-th metastable state; “I” represents length of a transmitting path of the laser light through the plasma; and “n_(m),” represents density of the atoms in the m-th metastable state. 